document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=118388>Question 118388</A>: <I><SPAN STYLE=\"word-break: break-all;\"> An electronic assembly consists of 2 sub systems A and B. from the previous testing procedures the following probabilities are known:<BR>\n" );
document.write( "P(A fails)=0.2<BR>\n" );
document.write( "P(B fails alone)=0.15<BR>\n" );
document.write( "P(A and B fails)=0.15<BR>\n" );
document.write( "evaluate P(A fails given B fails) {conditional probability}<BR>\n" );
document.write( "and<BR>\n" );
document.write( "P(A fails alone). </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #86505 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=86505\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> P(A fails)=0.2<BR>\n" );
document.write( "P(B fails alone)=0.15<BR>\n" );
document.write( "P(A and B fails)=0.15<BR>\n" );
document.write( "evaluate P(A fails given B fails) ------------------<BR>\n" );
document.write( "and<BR>\n" );
document.write( "P(A fails alone).<BR>\n" );
document.write( "--------<BR>\n" );
document.write( "An electronic assembly consists of 2 sub systems A and B. from the previous testing procedures the following probabilities are known:<BR>\n" );
document.write( "P(A fails)=0.2<BR>\n" );
document.write( "P(B fails alone)=0.15<BR>\n" );
document.write( "P(A and B fails)=0.15<BR>\n" );
document.write( "evaluate P(A fails given B fails) {conditional probability}<BR>\n" );
document.write( "and<BR>\n" );
document.write( "P(A fails alone).<BR>\n" );
document.write( "-------------------<BR>\n" );
document.write( "P(A fails | B fails) = [P(A fails and B fails)]/[P(B fails] = 0.15/P(B fails)<BR>\n" );
document.write( "but P(B fails) = P(B fails alone) + P(B fails and A fails) = 0.15 + 0.15 = 0.30<BR>\n" );
document.write( "So P(A fails|B fails) = 0.15/0.30 = 1/2<BR>\n" );
document.write( "-------------------------<BR>\n" );
document.write( "P(A fails alone) = P(A fails and B does not)<BR>\n" );
document.write( "=P(B does not fail|A fails)*P(A fails)<BR>\n" );
document.write( "=(1-P(A and B fails))*0.2<BR>\n" );
document.write( "=(1-0.15)*0.2<BR>\n" );
document.write( "=(0.85)*0.2<BR>\n" );
document.write( "= 0.17<BR>\n" );
document.write( "=================<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );